Size effects in nonpolar solvation: lessons from two simple models

Size dependence of the solute chemical potential mu(u) is examined using the Ornstein-Zernike equation for two models of the nonpolar solute-solvent interactions. Simple Lennard-Jones interactions are assumed in the first model while the Lennard-Jones potential is distributed over the solute volume in the second model similar to the Hamaker theory for the colloid dispersion forces. In both models, while mu(u) rises asymptotically as the third power of the solute size in agreement with asymptotic solution of the scaled particle theory, it increases faster at smaller sizes. Deviations from the cubic law are more pronounced at higher solvent densities and stronger molecular interactions. Within a relatively narrow size range typical for small organic molecules, mu(u) can be approximated with a polynomial of the third or even the second power. However, the latter approximation is less accurate and cannot be employed for extrapolation to the larger size region.